We construct our problem as a maximum likelihood optimization problem, similar to earlier works like word2vec [1]}, node2vec [2]} and OhmNet [3]}. We frame our method in such a way that it can be applied to (un)directed and (un)weighted networks also. Our method is a simple first step in a series of work to perform feature representation in a multiplex setup without requiring any hierarchy, like in [3]}, but the node representations still capture their neighborhood properties. Since a node can exist in many layers of a multiplex network, we assume that a node \(v\)  in layer \(i\)  can be related to neighbors of \(v\)  from other layers such as \(j,k,l,\dots \)  based on a probability ratio \(p\) .
